# connecticut core standards for mathematics

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Connecticut Core Standards for Mathematics. Systems of Professional Learning. Module 3 Grades K–5: Focus on Teaching and Learning. Focus on Teaching and Learning. By the end of this session you will have: Strengthened your working relationship with peer Core Standards Coaches. - PowerPoint PPT PresentationTRANSCRIPT

CT Systems of Professional Learning

Connecticut Core Standards for MathematicsSystems of Professional LearningModule 3 Grades K5: Focus on Teaching and Learning

(Slides 15, including the pre-assessment, will take about 10 minutes total.)1Focus on Teaching and LearningBy the end of this session you will have:Strengthened your working relationship with peer Core Standards Coaches. Deepened your understanding of the Practice and Content standards specified in the CCS-Math.Articulate a common understanding of UDL.Identified the importance of incorporating UDL practices into lessons. Described the alignment of instructional practices and learning expectations of the CCS-Math. 2

Review the outcomes for the day, sharing what you hope to accomplish throughout the full day session. There are nine outcomes for this session. These are presented to the participants over two slides. Public Consulting Group5/13/2014www.publicconsultinggroup.com2Focus on Teaching and Learning (cont'd)By the end of this session you will have:Planned for implementing UDL strategies within classroom lessons. Measured progress towards learning targets using the formative assessment process. Explored strategies for supporting teachers as they make changes to their classroom practices. Made plans for next steps in your CCS-Math implementation. 3

There are nine outcomes for this session. These are presented to the participants over two slides.

Public Consulting Group5/13/2014www.publicconsultinggroup.com3Morning SessionWelcome and IntroductionsSharing Implementation ExperiencesBuilding a Teaching and Learning Framework through UDLTeaching and Learning with the UDL PrinciplesAfternoon SessionSupporting Teachers with UDLAssessing Learning ProgressStudents Role in the Assessment ProcessMoving Forward with the CCS-Math ImplementationPost-Assessment, Session Evaluation, & Wrap UpTodays Agenda4

Review the agenda letting participants know that this is the pathway they will travel in order accomplish the nine outcomes discussed earlier. Note that in addition to the break for lunch, there will also be shorts breaks throughout the day, but participants should feel free to take a personal break as needed. Emphasize the importance of coming back from lunch and breaks on time to ensure enough time to complete all the work of the day. Public Consulting Group5/13/2014www.publicconsultinggroup.com4

Introductory Activity:Pre-Assessment CCS-MathPlease complete the Pre-Assessment5Page 5

This will be a short self-assessment, which will be found in the Participant Guide on page 5. It will assess where the coaches are now with the understanding of implementing the Practice Standards that were introduced in Module 1, and assess where they are in understanding the Content Standards. The participants will complete the same assessment at the end of the session. Allow 34 minutes to complete.Public Consulting Group5/13/2014www.publicconsultinggroup.com5Sharing Implementation ExperiencesSection 1

Page7Section 1: Sharing Implementation ExperiencesSection 1 Time: 30 Minutes

Section 1 Training Objectives: To review the key ideas developed in the Standards for Mathematical Content in Module 2. To share, discuss, and address experiences with, and common challenges of, supporting teachers in implementing the Standards for Mathematical Practice and Standards for Mathematical Content.

Section 1 Outline: The facilitator will begin by reviewing the key ideas developed on the Standards for Mathematical Content in Module 2.In groups, participants will share experiences and describe any aha moments from their continued implementation of the Standards for Mathematical Practice (SMP) and with assisting teachers with strategies for teaching the Standards for Mathematical Content. Participants will look for themes or choose one or two important successes, challenges, and/or insights to share with the larger group. These will be recorded on chart paper so that common themes and additional strategies can be discussed as a large group. Participants can record new ideas on the handout Moving Forward with the Content Standards. The facilitator will wrap up Section 1 by explaining that to build upon their knowledge and experience with the CCS-Math thus far, participants will begin to connect instructional strategies discussed in Modules 1 and 2 to a more focused teaching and learning framework derived from considerations within Universal Design for Learning, and begin to discuss connections between teaching, learning, and formative assessments.

Supporting DocumentsMoving Forward with the Content StandardsMaterialsChart paperMarkers

Public Consulting Group5/13/2014www.publicconsultinggroup.com6In Module 2 you:Examined the implications of the language of the content standards for teaching and learning. Analyzed the progression of topics in the content standards both within and across grade levels. Identified and modified CCS-aligned tasks that combine both the content and practice standards. Explored strategies for supporting teachers as they make changes to their classroom practices. Module 2 Review7

Review the four objectives of Module 2 with participants. As you quickly go through slides 718 you will support each bullet one-by-one with key slides from the Module 2 PowerPoint. Begin here with the first bulleted objective.

Examined the implications of the language of the content standards for teaching and learning. Remind participants that they discussed the differences of and connections between conceptual understanding, procedural skill and fluency, and application of mathematics. Use slides 810 to support this objective.

7Conceptual Understanding8Conceptual understanding refers to an integrated and functional grasp of mathematical ideas.

Adding it Up: Helping Children Learn Mathematics (2001)

Conceptual UnderstandingReview the quote on the slide, as well as the quote provided to participants in their Module 2 Participant Guide.

Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples of concepts; use and interrelate models, diagrams, manipulatives, and varied representations of concepts; identify and apply principles; know and apply facts and definitions; compare, contrast, and integrate related concepts and principles; recognize, interpret, and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding reflects a students ability to reason in settings involving the careful application of concept of definitions, relations, or representations of either. (Balka, Hull, & Harbin Miles, n.d.)

85/13/2014www.publicconsultinggroup.comPublic Consulting GroupProcedural Skill and Fluency9Procedural skill and fluency is demonstrated when students can perform calculations with speed and accuracy. Achieve the CoreFluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for higher-level thinking. EngageNY

Procedural Skill and FluencyReview the quotes on the slide. 95/13/2014www.publicconsultinggroup.comPublic Consulting GroupThe Standards call for students to use math flexibly for applications. Teachers provide opportunities for students to apply math in authentic contexts. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content. Application of Mathematics10Frieda & Parker (2012)Achieve the Core (2012)

Application of MathematicsGo through points on the slide. Ask participants how they have had students apply mathematics. Get two or three examples. Ask participants why this is important.

Application of mathematics is important because without this step or expectation students are learning math as a set of rules, procedures, etc. that have no real meaning in the world outside of the classroom. Students need to learn how math works and how it is used. Note here that when the conversation of application of mathematics typically comes up the phrase real-world problems is usually somewhere in the conversation. As teachers think about the types of problems that students will solve in order to apply their mathematical understanding, have them think about problems that would be real world to their students. This means that the problems should be contextually relevant and easily understood by the students at their particular grade level. Also note that, just as we saw with the fluency standard, not all standards focus on application. But, when the standard does point to solving problems through an application of mathematics, we really want to see how students can flexibly use what they know and understand. Finally, ask participants to briefly discuss how they can engage students in authentic problem-solving scenarios.

Before moving to the next slide that has examples of contextually relevant problems, focus participants on the third bullet on the slide and ask for one or two volunteers to give examples of how the CCS-Math standards can be supported and connected to the standards from other content areas in order for students to see and apply mathematics outside of their typical math lesson time. 105/13/2014www.publicconsultinggroup.comPublic Consulting GroupModule 2 ReviewIn Module 2 you:Examined the implications of the language of the content standards for teaching and learning. Analyzed the progression of topics in the content standards both within and across grade levels. Identified and modified CCS-aligned tasks that combine both the content and practice standards. Explored strategies for supporting teachers as they make changes to their classroom practices. 11

Review the second bulleted objective: Analyzed the progression of topics in the content